Problem: Solve for $x$ and $y$ using elimination. ${-3x+5y = 29}$ ${-3x+6y = 39}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${3x-5y = -29}$ $-3x+6y = 39$ Add the top and bottom equations together. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+5y = 29}\thinspace$ to find $x$ ${-3x + 5}{(10)}{= 29}$ $-3x+50 = 29$ $-3x+50{-50} = 29{-50}$ $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {-3x+6y = 39}\thinspace$ and get the same answer for $x$ : ${-3x + 6}{(10)}{= 39}$ ${x = 7}$